def Morison_added_mass(w, draft, radius, Cm=2.0):
"""Calculate added mass and damping from Morison strip model of
uniform cylinder"""
from whales.viscous_drag import ViscousDragModel
Morison_model = ViscousDragModel({
'inertia coefficient':
Cm,
'members': [{
'end1': [0, 0, 0],
'end2': [0, 0, -draft],
'diameter': 2 * radius,
'strip width': 1.0,
}]
})
A1 = Morison_model.Morison_added_mass()
A = np.tile(A1, (len(w), 1, 1))
return LinearSystem(A, zeros_like(A), zeros_like(A))
def added_mass(w, z1, z2, diameter, Cm=2):
"""Calculate the added mass/damping. Specific for now to vertical
cylinders of varying diameter.
``z1``, ``z2``: coordinates of ends of element
``diameter``: array (2 x Npoints) diameter at each z value
"""
config = {
'end1': [0, 0, z1],
'end2': [0, 0, z2],
'diameter': diameter,
'strip width': 1.0,
}
Morison_model = ViscousDragModel({
'inertia coefficient': Cm,
'members': [config],
})
A1 = Morison_model.Morison_added_mass()
A = np.tile(A1, (len(w), 1, 1))
return LinearSystem(A, zeros_like(A), zeros_like(A))
class CylinderTestCase(MyTestCase):
"""Test simple model with vertical cylinder"""
def setUp(self):
config = {
'drag coefficient': 0.7,
'inertia coefficient': 2.0,
'members': [{
'end1': [0, 0, 0],
'end2': [0, 0, -10],
'diameter': 2.3,
'strip width': 1,
}],
}
self.model = ViscousDragModel(config)
def test_model_elements(self):
"""Check element strips setup correctly"""
m = self.model
self.assertArraysEqual(m.element_lengths, np.ones(10))
# Centres of strips
centres = np.zeros((10, 3))
centres[:,2] = -np.arange(0.5, 10, 1)
self.assertArraysEqual(m.element_centres, centres)
# Element diameters
self.assertArraysEqual(m.element_diameters, 2.3)
# Element axes
self.assertArraysEqual(m.element_axes, np.array([np.eye(3)] * 10))
def test_wave_velocity_transfer_func(self):
"""Test wave velocity transfer function"""
w = np.array([1,2]) # frequencies to test
H_uf = self.model.wave_velocity_transfer_function(w)
# With waves in x-direction, sideways velocity should be zero
self.assertArraysEqual(H_uf[:,:,1], 0)
# Check variation in depth: exp(kz)
iz1 = 3
iz2 = 8
z = self.model.element_centres[:,2]
for i in range(2):
assert_array_almost_equal_nulp(H_uf[i,iz1,:] / np.exp(w[i]**2/9.81*z[iz1]),
H_uf[i,iz2,:] / np.exp(w[i]**2/9.81*z[iz2]))
# Check all x velocities are in-phase and real, all z are imaginary
self.assertTrue(np.isreal( H_uf[:,:,0]).all())
self.assertTrue(np.isreal(1j * H_uf[:,:,2]).all())
def test_structural_velocity_transfer_func(self):
"""Test structural velocity with special cases"""
w = np.array([1,2]) # frequencies to test
# Case 1: pure surge motion
H1 = np.zeros((2, 6)) # shape (freq, xyzXYZ)
H1[:,0] = 1 # maximum surge at maximum datum wave height
H_us = self.model.structural_velocity_transfer_function(w, H1)
# all elements should have same surge velocity; all other velocities zero
# at t=0, velocity is zero and becoming negative 90 deg later
self.assertArraysEqual(H_us[1,:,0], 2j)
self.assertArraysEqual(H_us[0,:,0], 1j)
self.assertArraysEqual(H_us[:,:,1:], 0)
# Case 2: pure roll motion
H2 = np.zeros((2, 6)) # shape (freq, xyzXYZ)
H2[:,3] = 1 # maximum roll at maximum datum wave height
H_us = self.model.structural_velocity_transfer_function(w, H2)
# x & z velocity should be zero
self.assertArraysEqual(H_us[:,:,[0,2]], 0)
# y velocity corresponding to rotation about origin (check bottom)
# at t=0, ang. velocity is zero and becoming negative 90 deg later
# Velocity of bottom element = 9.5 * ang vel
self.assertArraysEqual(H_us[0,-1,1], 9.5 * 1j)
self.assertArraysEqual(H_us[1,-1,1], 9.5 * 2j)
def test_added_mass(self):
"""Test added mass calculation from Morison elements"""
A = self.model.Morison_added_mass()
# Expected surge added mass: (Cm-1) * rho * V
self.assertEqual(A[0,0], 1 * 1025 * 10 * np.pi * 2.3**2 / 4)
